I'd argue this is, if we're talking about practicality, is just crumbs though.
For example, scratch-resistant lenses were developed at NASA. Proving that it could be done wasn't the important factor that brought it to everyone's homes. What brought it to everyone's homes was the fact that NASA licensed
As another example, single-crystal silicon solar cells were first developed after NASA sponsored a 28-member coalition to develop an unmanned, high altitude aircraft. Private companies don't create coalitions like this and are much less likely to license or waive patents.
[1]: https://en.wikipedia.org/wiki/NASA_spinoff_technologies#Scra...
And proving it can be done is aside from proving how it can be done. Once the general principle is proven out, competitors find ways to apply it that avoid infringing on the patent. The process of discovering the how involves expensive trial and error, that a large private sector can greatly accelerate.
I agree that publicly funded technology initiatives have their own strengths, but private technology provide far more than crumbs. Much of an industry's development is in the form of mundane, that is too unremarkable to be patented or held in secret, and for that, it makes no difference what the source of the funding is.
Much of what is developed is in the public domain. Patents and trade secrets only go so far. You can't patent or keep secret the concepts that these trials prove out.
The satellite of industries that develops to support space flight is also not affected by whether the fights they're supporting are private vs government, and neither are the skills developed by the engineers working these projects.
Private also has one distinct advantage: it can be self-sustaining, in being managed by an owner with a strong stake in the venture as a business unit.